Class summary: Monday, 2/24
I started an "Interlude" on counting techniques and combinatorial
probabilities. This material is not adequately covered in the Pitman
text (some of it can be found in Appendix I and in Section 2.5,under
"Sampling without replacement"),
so I distributed a handout with a couple of pages
xeroxed from another text (Hoel/Port/Stone). (This handout is not
available online.)
There are two basic counting formulas, depending on whether order is taken
into account or not: Counting
k-combinations (or unordered samples, or subsets of size k)
of n elements, and counting
k-permutations (or ordered samples) of n elements. You should know these
formulas and the relation between them (the latter is k! times the
former).
I did one example (if 8 distinct days of the year are selected at random,
what is the probability that all 8 days fall into distinct months?),
first by counting Omega and A using unordered samples, and
then by taking order into account in counting the number of elements in
Omega and in A.
Counting ordered samples is, in most situations,
the better approach, and is much safer than counting unordered samples.
Also, whatever method you use, be sure to count Omega and A by the same
method.
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